IEEE Transactions on Information Theory最新文献

{"title":"Criss-Cross Deletion Correcting Codes: Optimal Constructions With Efficient Decoders","authors":"Yubo Sun;Gennian Ge","doi":"10.1109/TIT.2026.3696242","DOIUrl":"https://doi.org/10.1109/TIT.2026.3696242","url":null,"abstract":"This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for <italic>criss-cross deletions</i>. We consider an <inline-formula> <tex-math>$ n times n $ </tex-math></inline-formula> array <inline-formula> <tex-math>$boldsymbol {X}$ </tex-math></inline-formula> over a <inline-formula> <tex-math>$ q $ </tex-math></inline-formula>-ary alphabet <inline-formula> <tex-math>$Sigma _{q}:= {0, 1, ldots, q-1}$ </tex-math></inline-formula> that is subject to a <inline-formula> <tex-math>$(t_{r}, t_{c})$ </tex-math></inline-formula><italic>-criss-cross deletion</i>, which involves the simultaneous removal of <inline-formula> <tex-math>$ t_{r} $ </tex-math></inline-formula> rows and <inline-formula> <tex-math>$ t_{c} $ </tex-math></inline-formula> columns. A code <inline-formula> <tex-math>$mathcal {C} subseteq Sigma _{q}^{n times n}$ </tex-math></inline-formula> is defined as a <inline-formula> <tex-math>$(t_{r},t_{c})$ </tex-math></inline-formula><italic>-criss-cross deletion correcting code</i> if it can successfully correct these deletions. Our primary technical contributions are as follows: 1) Theoretical Bounds: We derive a sphere-packing type lower bound and a Gilbert-Varshamov type upper bound on the redundancy of optimal codes. Our results indicate that the optimal redundancy for a <inline-formula> <tex-math>$(t_{r}, t_{c})$ </tex-math></inline-formula>-criss-cross deletion correcting code lies between <inline-formula> <tex-math>$(t_{r} + t_{c})nlog q + (t_{r} + t_{c})log n + O_{q,t_{r},t_{c}}(1)$ </tex-math></inline-formula> and <inline-formula> <tex-math>$(t_{r} + t_{c})nlog q + 2(t_{r} + t_{c})log n + O_{q,t_{r},t_{c}}(1)$ </tex-math></inline-formula>, where the logarithm is on base two, and <inline-formula> <tex-math>$O_{q,t_{r},t_{c}}(1)$ </tex-math></inline-formula> is a constant that depends solely on <inline-formula> <tex-math>$q$ </tex-math></inline-formula>, <inline-formula> <tex-math>$t_{r}$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$t_{c}$ </tex-math></inline-formula>. 2) Optimal Constructions: For the case of <inline-formula> <tex-math>$(1,1)$ </tex-math></inline-formula>-criss-cross deletions, we propose two families of constructions that achieve <inline-formula> <tex-math>$2nlog q + 2log n + O_{q}(1)$ </tex-math></inline-formula> bits of redundancy. This redundancy is optimal up to an additive constant term <inline-formula> <tex-math>$O_{q}(1)$ </tex-math></inline-formula>, which depends solely on <inline-formula> <tex-math>$q$ </tex-math></inline-formula>. One family is designed for non-binary alphabets, while the other addresses arbitrary alphabets. For the case of <inline-formula> <tex-math>$(t_{r}, t_{c})$ </tex-math></inline-formula>-criss-cross deletions, we provide a strategy to derive optimal codes when both unidirectional deletions occur consecutively. 3) Efficient Decoders: We propose decoding algorithms with a time complexity of <inline-formula> <tex-math","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4648-4660"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Binary Dispersed Array Codes for Distributed Storage Systems","authors":"Qin Huang;Guanchen He;Fuqiang Sun","doi":"10.1109/TIT.2026.3689964","DOIUrl":"https://doi.org/10.1109/TIT.2026.3689964","url":null,"abstract":"This paper proposes to construct binary array codes from nonbinary codes by binary matrix dispersion. Thanks to their low-density and quasi-cyclic generator matrices, these <italic>binary dispersed array codes</i> (BDACs) enjoy low encoding complexity. Their reconstruction property is characterized through matrix transformation. Several explicit constructions of BDACs from minimum-bandwidth regenerating codes, piggybacking codes, and locally recoverable codes are presented, as well as their similar single-node repair strategies to their nonbinary counterparts.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4695-4709"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved Gilbert–Varshamov Bound for Sum-Rank-Metric Codes via Graph Theory","authors":"Aida Abiad;Harper Reijnders;Michael Tait","doi":"10.1109/TIT.2026.3691929","DOIUrl":"https://doi.org/10.1109/TIT.2026.3691929","url":null,"abstract":"We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that asymptotically <inline-formula> <tex-math>$mathbb {F}_{q}^{mathbf {n}times mathbf {m}}$ </tex-math></inline-formula> can be partitioned into sum-rank-metric codes whose average size is bigger than the GV bound by a logarithmic factor for these parameters. Finally, we discuss the connection of such codes to set-coloring Ramsey numbers.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4828-4836"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction","authors":"Yubo Sun;Gennian Ge","doi":"10.1109/TIT.2026.3694157","DOIUrl":"https://doi.org/10.1109/TIT.2026.3694157","url":null,"abstract":"Let &lt;inline-formula&gt; &lt;tex-math&gt;$mathcal {B}(cdot)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; be an error ball function. A set of &lt;inline-formula&gt; &lt;tex-math&gt;$q$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-ary sequences of length &lt;inline-formula&gt; &lt;tex-math&gt;$n$ &lt;/tex-math&gt;&lt;/inline-formula&gt; is referred to as an &lt;inline-formula&gt; &lt;tex-math&gt;$(n,q,N;mathcal {B})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;&lt;italic&gt;-reconstruction code&lt;/i&gt; if each sequence &lt;inline-formula&gt; &lt;tex-math&gt;$boldsymbol {x}$ &lt;/tex-math&gt;&lt;/inline-formula&gt; within this set can be uniquely reconstructed from any &lt;inline-formula&gt; &lt;tex-math&gt;$N$ &lt;/tex-math&gt;&lt;/inline-formula&gt; distinct elements within its error ball &lt;inline-formula&gt; &lt;tex-math&gt;$mathcal {B}(boldsymbol {x})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. The main objective in this area is to determine or establish bounds for the minimum redundancy of &lt;inline-formula&gt; &lt;tex-math&gt;$(n,q,N;mathcal {B})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-reconstruction codes, denoted by &lt;inline-formula&gt; &lt;tex-math&gt;$rho (n,q,N;mathcal {B})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. In this paper, we investigate reconstruction codes where the error ball corresponds to either the &lt;inline-formula&gt; &lt;tex-math&gt;$t$ &lt;/tex-math&gt;&lt;/inline-formula&gt;&lt;italic&gt;-deletion ball&lt;/i&gt; &lt;inline-formula&gt; &lt;tex-math&gt;$mathcal {D}_{t}(cdot)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; or the &lt;inline-formula&gt; &lt;tex-math&gt;$t$ &lt;/tex-math&gt;&lt;/inline-formula&gt;&lt;italic&gt;-insertion ball&lt;/i&gt; &lt;inline-formula&gt; &lt;tex-math&gt;$mathcal {I}_{t}(cdot)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Our primary technical contributions include: 1) establishing a fundamental connection between reconstruction codes for deletions and insertions. Specifically, for any positive integers &lt;inline-formula&gt; &lt;tex-math&gt;$n,t,q,N$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, any &lt;inline-formula&gt; &lt;tex-math&gt;$(n,q,N;mathcal {I}_{t})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-reconstruction code is also an &lt;inline-formula&gt; &lt;tex-math&gt;$(n,q,N;mathcal {D}_{t})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-reconstruction code. This leads to the inequality &lt;inline-formula&gt; &lt;tex-math&gt;$rho (n,q,N;mathcal {D}_{t})leq rho (n,q,N;mathcal {I}_{t})$ &lt;/tex-math&gt;&lt;/inline-formula&gt;; 2) identifying a significant distinction between reconstruction codes for deletions and insertions when &lt;inline-formula&gt; &lt;tex-math&gt;$N=O(n^{t-1})$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$tgeq 2$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. For deletions, we prove that there exists some constant &lt;inline-formula&gt; &lt;tex-math&gt;$K$ &lt;/tex-math&gt;&lt;/inline-formula&gt; such that &lt;inline-formula&gt; &lt;tex-math&gt;$rho left ({ n,q,tfrac {2(q-1)^{t-1}}{q^{t-1}(t-1)!}n^{t-1}+K n^{t-2};mathcal {D}_{t}}right)=O(1)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, which disproves a conjecture posed by Chrisnata et al. (2022). In contrast, for insertions, we show that there exists some constant &lt;inline-formula&gt; &lt;tex-math&gt;$K'$ &lt;/tex-math&gt;&lt;/inline-formula&gt; such that &lt;inline-formula&gt; &lt;tex-math&gt;$rho left ({ n,q,tfrac {(q-1)^{t-1}}{(t-1)!}n^{t-1}+K' n^{t-2};mathcal {I}_{t}}right)=log log n + O(1)$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, which extends a key result by Ye et ","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4739-4750"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148508182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Walsh Spectra of Quadratic APN Functions","authors":"Sophie Hannah Bénéteau;Nicolas Goluboff;Lukas Kölsch;Divyesh Vaghasiya","doi":"10.1109/TIT.2026.3695003","DOIUrl":"https://doi.org/10.1109/TIT.2026.3695003","url":null,"abstract":"APN functions provide optimal resistance to differential attacks when used as building blocks in block ciphers and are thus of great theoretical interest. One of the most important properties of APN functions is their linearity, which is directly related to the Walsh spectrum of the function. In this paper, we establish two novel connections that allow us to derive strong conditions on the Walsh spectra of quadratic APN functions. We prove that the Walsh transform of a quadratic APN function <inline-formula> <tex-math>$F$ </tex-math></inline-formula> operating on <inline-formula> <tex-math>$n=2k$ </tex-math></inline-formula> bits is uniquely associated with a vector space partition of <inline-formula> <tex-math>$mathbb {F}_{2}^{n}$ </tex-math></inline-formula> and a specific blocking set in the corresponding projective space <inline-formula> <tex-math>$mathop {mathrm {PG}}nolimits (n-1,2)$ </tex-math></inline-formula>. These connections allow us to prove a variety of results on the Walsh spectrum of <inline-formula> <tex-math>$F$ </tex-math></inline-formula>. We prove for instance that <inline-formula> <tex-math>$F$ </tex-math></inline-formula> can have at most one component function of amplitude larger than <inline-formula> <tex-math>$2^{3n/4}$ </tex-math></inline-formula>. We also find the first nontrivial upper bound on the number of bent component functions of a quadratic APN function, and provide conditions for a function to be CCZ-equivalent to a permutation based on its number of bent components.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5207-5216"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypothesis Testing for Adversarial Channels: Chernoff–Stein Exponents","authors":"Eeshan Modak;Neha Sangwan;Mayank Bakshi;Bikash Kumar Dey;Vinod M. Prabhakaran","doi":"10.1109/TIT.2026.3691175","DOIUrl":"https://doi.org/10.1109/TIT.2026.3691175","url":null,"abstract":"Consider the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the inputs to the channel. Given the hypothesis, from the set associated with the hypothesis, an adversary chooses channels, one for each element of the input vector. Based on the channel outputs, a detector attempts to distinguish between the hypotheses. For the fixed-length setting, we study the Chernoff-Stein exponent for the cases where the transmitter (i) is deterministic, (ii) may privately randomize, and (iii) shares randomness with the detector that is unavailable to the adversary. It turns out that while a memoryless transmission strategy is optimal under shared randomness, it may be strictly suboptimal when the transmitter only has private randomness. We also study the sequential version of this problem in each of the three settings and show that both the Chernoff-Stein exponents can be simultaneously achieved.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5104-5121"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Information Theoretic Fairness: From Perfect to Bounded Demographic Parity","authors":"Amirreza Zamani;Abolfazl Changizi;Mikael Skoglund","doi":"10.1109/TIT.2026.3693890","DOIUrl":"https://doi.org/10.1109/TIT.2026.3693890","url":null,"abstract":"In this paper, we study the fundamental limits in the design of fair representations under different demographic (statistical) parity constraints through the lens of information theory. We first consider the design problem achieving perfect demographic parity. More specifically, an agent uses some useful data &lt;inline-formula&gt; &lt;tex-math&gt;$X$ &lt;/tex-math&gt;&lt;/inline-formula&gt; to solve a task &lt;inline-formula&gt; &lt;tex-math&gt;$T$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Since both &lt;inline-formula&gt; &lt;tex-math&gt;$X$ &lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt; &lt;tex-math&gt;$T$ &lt;/tex-math&gt;&lt;/inline-formula&gt; are correlated with some sensitive attribute or secret &lt;inline-formula&gt; &lt;tex-math&gt;$S$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, the agent designs a representation &lt;inline-formula&gt; &lt;tex-math&gt;$Y$ &lt;/tex-math&gt;&lt;/inline-formula&gt; that has no information about the sensitive attribute &lt;inline-formula&gt; &lt;tex-math&gt;$S$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, i.e., satisfying perfect demographic parity constraint, implying that &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;S)=0$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. We then relax the perfect demographic parity and consider a bounded-parity constraint, implying that &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;S) leq epsilon $ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Under perfect demographic parity, we consider two scenarios. First, we consider a design problem where we want to maximize the information &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;T)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; that the representation contains about the task, while constraining the level of compression (or encoding rate), that is, ensuring that &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;X) leq r$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Second, inspired by the Conditional Fairness Bottleneck problem, we consider a design problem where we want to maximize the information &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;T|S)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; that the representation contains about the task which is not shared by the sensitive attribute, while constraining the amount of irrelevant information, that is, ensuring that &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;X|T,S) leq r$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Under bounded demographic parity, we design &lt;inline-formula&gt; &lt;tex-math&gt;$Y$ &lt;/tex-math&gt;&lt;/inline-formula&gt; that maximizes the mutual information &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;T)$ &lt;/tex-math&gt;&lt;/inline-formula&gt; about the task while satisfying a bounded compression (or encoding rate) constraint, that is, ensuring that &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;X) leq r$ &lt;/tex-math&gt;&lt;/inline-formula&gt;. Simultaneously, &lt;inline-formula&gt; &lt;tex-math&gt;$Y$ &lt;/tex-math&gt;&lt;/inline-formula&gt; satisfies the bounded demographic parity constraint &lt;inline-formula&gt; &lt;tex-math&gt;$I(Y;S) leq epsilon $ &lt;/tex-math&gt;&lt;/inline-formula&gt;. To design &lt;inline-formula&gt; &lt;tex-math&gt;$Y$ &lt;/tex-math&gt;&lt;/inline-formula&gt;, we use extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma which are based on randomization techniques and study the tightness of the obtained bounds in special cases. Every design problem ","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"5122-5138"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148512148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2026.3698701","DOIUrl":"https://doi.org/10.1109/TIT.2026.3698701","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"C3-C3"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11574011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148442215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimality of Meta-Converse for Channel Simulation","authors":"Aadil Oufkir;Omar Fawzi;Mario Berta","doi":"10.1109/TIT.2026.3689356","DOIUrl":"https://doi.org/10.1109/TIT.2026.3689356","url":null,"abstract":"We study the effect of shared non-signaling correlations for the problem of simulating a channel using noiseless communication in the one-shot setting. For classical channels, we show how to round any non-signaling-assisted simulation strategy — which corresponds to the natural linear programming meta-converse for channel simulation — to a strategy that only uses shared randomness. For quantum channels, we round any non-signaling-assisted simulation strategy to a strategy that only uses shared entanglement. Our main result is for classical and classical-quantum channels, for which we employ ideas from approximation algorithms to give a guarantee on the ratio of success probabilities of at least <inline-formula> <tex-math>$(1-mathrm {e}^{-1})$ </tex-math></inline-formula>. We further show this ratio to be optimal for the purely classical case. It can be improved to <inline-formula> <tex-math>$(1-t^{-1})$ </tex-math></inline-formula> using <inline-formula> <tex-math>$O(ln ln (t))$ </tex-math></inline-formula> additional bits of communication.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4522-4536"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148504451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sibson α-Mutual Information and Its Variational Representations","authors":"Amedeo Roberto Esposito;Michael Gastpar;Ibrahim Issa","doi":"10.1109/TIT.2025.3587340","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587340","url":null,"abstract":"Information measures can be constructed from Rényi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>-mutual information and has received renewed attention recently in several contexts: concentration of measure under dependence, statistical learning, hypothesis testing, and estimation theory. In this paper, we survey and extend the state of the art. In particular, we introduce variational representations for Sibson <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>-mutual information and employ them in each described context to derive novel results. Namely, we produce generalized Transportation-Cost inequalities and Fano-type inequalities. We also present an overview of known applications, spanning from learning theory and Bayesian risk to universal prediction.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 7","pages":"4434-4467"},"PeriodicalIF":2.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}